The Wiener number of a connected graph is equal to the sum of distances between all pairs of its vertices. A graph formed by a row of n hexagonal cells is called an n-hexagonal chain. Wiener number of an n x m hexagonal rectangle was found by the authors. An n x m hexagonal jagged-rectangle whose shape forms a rectangle and the number of hexagonal cells in each chain alternate between n and n 1...

In this note, we study the degree distance of a graph which is a degree analogue of the Wiener index. Given n and e, we determine the minimum degree distance of a connected graph of order n and size e.

The general Randić index Rα(G) is the sum of the weights (dG(u)dG(v)) over all edges uv of a (molecular) graph G, where α is a real number and dG(u) is the degree of the vertex u of G. In this paper, for any real number α ≤ −1, the minimum general Randić index Rα(T ) among all the conjugated trees (trees with a Kekulé structure) is determined and the corresponding extremal conjugated trees are ...

Content centric networking (CCN) is a newly proposed futuristic Internet paradigm in which communication depends on the decoupling of content names from their locations. In CCN-based multihop wireless ad hoc networks, the participating nodes show dynamic topology, intermittent connectivity, channels fluctuation, and severe constraints such as limited battery power. In the case of traffic conges...

Futuristic computers will only be thought of in the context of their ubiquitous connectivity. Net-centric computing isn’t communications or networking per se, although it certainly includes both. With the changes in the computing and networking environment we need a different paradigm for distributed computing. The area of netcentric computing encompasses the embedded systems but is much larger...

Let G be a connected graph, nu(e) is the number of vertices of G lying closer to u and nv(e) is the number of vertices of G lying closer to v. Then the Szeged index of G is defined as the sum of nu(e)nv(e), over edges of G.. The PI index of G is a Szeged-like topological index defined as the sum of [mu(e)+ mv(e)], where mu(e) is the number of edges of G lying closer to u than to v, mv(e) is the...

The general Randić index Rα(G) of a graph G is defined as the sum of the weights (d(u)d(v)) α of all edges uv of G, where d(u) denotes the degree of a vertex u in G and α is an arbitrary real number. Clark and Moon gave the lower and upper bounds for the Randić index R −1 of all trees, and posed the problem to determine better bounds. In this paper we give the best possible lower and upper boun...

The Randić index R(G) of a graph G is the sum of weights (deg(u) deg(v))−0.5 over all edges uv of G, where deg(v) denotes the degree of a vertex v. We prove that for any tree T with n1 leaves R(T ) ≥ ad(T ) + max(0,n1 − 2), where ad(T ) is the average distance between vertices of T . As a consequence we resolve the conjecture R(G) ≥ ad(G) given by Fajtlowicz in 1988 for the case when G is a tree.

Let $G$ be a non-abelian group. The non-commuting graph $Gamma_G$ of $G$ is defined as the graph whose vertex set is the non-central elements of $G$ and two vertices are joined if and only if they do not commute.In this paper we study some properties of $Gamma_G$ and introduce $n$-regular $AC$-groups. Also we then obtain a formula for Szeged index of $Gamma_G$ in terms of $n$, $|Z(G)|$ and $|G|...